A crash in the housing market seemed inevitable during the early weeks of the COVID-19 recession. However, that bust didn't come to fruition, in fact, the opposite happened: A combination of government support, recession-induced low interest rates, and eager homebuyers set off a housing boom. Since the onset of the crisis, median home prices are up a staggering 24%.

But much of that government aid and support is about to go away. The foreclosure moratorium, which prevents foreclosures of federally-backed mortgages, will come to an end on July 31. Then on Sept. 30, the mortgage forbearance program, which allows some borrowers to pause their payments, will lapse. Since the beginning of the pandemic, over 7 million homeowners have been enrolled in the forbearance program. However, as the economy has improved that number has fallen. As of July 11, there are still 1.75 million borrowers, or 3.5% of U.S. mortgages, enrolled in the forbearance program.

The foreclosure crisis following the 2008 housing crash was so bad, in part, because tens of millions of financially strained homeowners were underwater (meaning a borrower's remaining mortgage balance is greater than the home's value) and had no choice but foreclosure. That's unlikely to be the case for financially strapped homeowners this year. These homeowners are likely sitting on sizable home equity (home value minus the outstanding mortgage), and if they can't repay the mortgage they can simply sell into the currently red-hot housing market.

If even a small fraction of the 1.75 million homeowners currently protected by the mortgage forbearance program opt to sell instead of going back to repaying their mortgage, it could have a big impact on the historically tight housing market. According to the National Association of Realtors, there are only 1.37 million units currently available for sale. Over the past four decades, the U.S. has averaged 2.5 million units at any given time. This year, housing inventory hit its lowest level since the data started getting tracked in the '80s.

"The wildcard in the supply landscape is what happens to the homes where the owners are in mortgage forbearance. Some will have returned to gainful employment and will work with their lenders to adjust the terms of their loan, allowing them to remain in their home. Others will not be so lucky and will lose their homes," Ali Wolf, chief economist at Zonda, a housing market research firm, told Fortune. "Unless the forbearance period is extended again, though, we should expect some of those homes to hit the market over the next year."

That begs the question: How many of these behind homeowners are likely to sell? To find out, Fortune asked researchers at Home.LLC, a startup that provides down payment assistance to homebuyers in return for a share of profits, to run the numbers. The finding? If the government doesn't extend the mortgage forbearance program, Home.LLC's model forecasts an additional 11% increase to housing inventory later this year. But that may not be enough to lower prices.

"High positive home equity among delinquent homeowners results in lower likelihood of foreclosure since people can refinance or sell the home to avoid defaulting on their mortgage," says Nik Shah, CEO of Home.LLC. Those who do choose to sell are unlikely to shift the market. The forecasted uptick in inventory, he says, "isn't much given that inventory is at a 40-year low. So, we project that home prices will continue to grow rapidly even if the forbearance program ends."

While a lapse of the mortgage forbearance program is likely, it isn't guaranteed. The benefit, initially created by the $2.2 trillion CARES Act in March 2020, has already been extended three times. The last extension came from the Biden administration in late June when it extended forbearance to Sept. 30. However, so far, the White House hasn't suggested another extension is looming.

"Many homeowners exiting mortgage forbearance are returning to their pre-pandemic earnings and are no longer facing financial hardship associated with the pandemic," the White House wrote in a statement on July 23. "For homeowners who can resume their pre-pandemic monthly mortgage payment and where agencies have the authority, agencies will continue requiring mortgage servicers to offer options that allow borrowers to move missed payments to the end of the mortgage at no additional cost to the borrower."